What we call corn today originated in Mexico and Central America as a type of grass. Through cross-pollination, it evolved into something similar to today's field corn and became a staple food throughout the American continent. Corn can be divided into the four basic groups of field, sweet, popcorn and ornamental, but sweet corn is much more popular with home gardeners than the other types. Sweet corn is pollinated by the wind and should be grown in blocks instead of long rows to ensure a better crop.
Peppers have been grown in South America since prehistoric times and were introduced to European tables by Christopher Columbus. Appreciated for their ornamental quality as well as flavor, peppers come in an array of colors and shapes, from large, many-lobed types to long and thin. Sweet peppers contain little to no capsaicin, the chemical which causes hot peppers to taste spicy, but sweet and hot peppers can cross-pollinate, and this will affect their flavor.
Cross-pollination is what happens when two different varieties of a species of plant interbreed. This affects the characteristics of the vegetables or fruits harvested from these plants. While corn and peppers will not cross with each other, corn will cross with other types of corn, and peppers with peppers. Corn is mechanically pollinated -- usually by the wind -- so field corn or popcorn will cross with sweet corn. Peppers are also wind-pollinated, but insects also play a role, and sweet and hot varieties will cross to produce sweet peppers with a tang and hot peppers that don't pack much of a punch.
Cross-pollination is only a problem if you plan to save your seeds and plant them the following season. Changes brought about by interbreeding will only show up in the next generation. If you want to avoid interbreeding, distance the varieties. You can plant blocks of corn at least 200 feet apart to avoid cross-pollination, or you can plant varieties that mature at different times. Isolation works for peppers, as well. Simply plant the sweet varieties and the hot varieties in different sections of the garden.